## Michigan Mathematical Journal

### Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups

Arash Ghaani Farashahi

#### Abstract

This paper presents a systematic study for classical aspects of functions with absolutely convergent Fourier series over homogeneous spaces of compact groups. Let $G$ be a compact group, $H$ be a closed subgroup of $G$, and $\mu$ be the normalized $G$-invariant measure over the left coset space $G/H$ associated with Weil’s formula with respect to the probability measures of $G$ and $H$. We introduce the abstract notion of functions with absolutely convergent Fourier series in the Banach function space $L^{1}(G/H,\mu)$. We then present some analytic characterizations for the linear space consisting of functions with absolutely convergent Fourier series over the compact homogeneous space $G/H$.

#### Article information

Source
Michigan Math. J., Volume 69, Issue 1 (2020), 179-200.

Dates
Revised: 24 April 2018
First available in Project Euclid: 21 November 2019

https://projecteuclid.org/euclid.mmj/1574326881

Digital Object Identifier
doi:10.1307/mmj/1574326881

Mathematical Reviews number (MathSciNet)
MR4071349

Zentralblatt MATH identifier
07208929

#### Citation

Ghaani Farashahi, Arash. Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups. Michigan Math. J. 69 (2020), no. 1, 179--200. doi:10.1307/mmj/1574326881. https://projecteuclid.org/euclid.mmj/1574326881

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